As typical scanning probe microscopes (SPMs), scanning tunnel microscopes (STMs) and atomic force microscopes (AFMs) have been known. Among these microscopes, AFMs are expected as a technique for observing, for example, the nano-functional dynamics of biological molecules.
Conventionally proposed typical AFMs comprise a cantilever having a probe at the free end, and a scanner that performs scanning of a sample stage. These AFMs sense displacement of the cantilever to control the scanner so as to maintain the distance between the probe and the sample.
An important objective of the AFM is to increase scan speed. In particular, observation of functional dynamics of biological molecules as described above needs to be achieved in a short time. This requires the scan speed to be increased.
In increasing the scan speed of the AFM, the scanner for the sample stage is the device whose performance is most difficult to be improved. A conventional scanner is composed of piezoelectric transducing element, called piezoactuator. While the cantilever has a microscopic size, the scanner has a macroscopic size. Because of the size of the scanner, it is difficult to increase the resonant frequency of the scanner. Accordingly, to avoid undesired vibration, scanning must be executed at lower frequencies than the resonant frequency of the scanner. Thus, the scanner has been a bottleneck for increasing in the speed of the AFM.
An active damping is widely used which is a control technique carrying out damping in accordance with the condition of a controlled object (displacement, speed, acceleration, or the like). The active damping is capable of eliminating or reducing the resonance of the controlled object.
An active Q-control method is known as an active damping method. The active Q-control method carries out damping by differentiating a vibration signal detected in the controlled object (control target), inverting the plus and minus sign of the differentiated signal, and adding the resultant signal to a driving signal, thereby increasing an apparent viscous resistance. However, this ordinary active damping method is not sufficiently effective on a resonant system such as a scanner having plural resonant components connected in parallel, accordingly considerably large resonant components may remain.
The conventional active damping method will be described in further detail. Here, first, the principle of an active-control method will be described. The simplest resonant system has a transfer function G(s) expressed by a second-order low pass filter, that is, indicated in equation (1).
                              G          ⁡                      (            s            )                          =                              ω            0            2                                              s              2                        +                                                            ω                  0                                Q                            ⁢              s                        +                          ω              0              2                                                          (        1        )            
In this system, the Q value can be reduced by performing an operation shown in the block diagram in FIG. 1. The Q value (Quality Factor) refers to an amount indicating the sharpness of a resonant spectrum. The Q value increases consistently with decreasing viscous resistance of the resonant system. In contrast, the Q value decreases consistently with increasing viscous resistance. The configuration shown in FIG. 1 differentiates an output signal Uout from a system described by a transfer function G(s), inverts the plus and minus sign of the differentiated signal (−D(s)), applies a gain to the plus-minus-inverted signal, and adds the resultant signal to an input signal (driving signal) Uin.
In FIG. 1, a differentiating operation D(s) is s/ω0. A transfer function indicating the input-output (I/O) relationship in FIG. 1 is as shown below.
                                          G            ′                    ⁡                      (            s            )                          =                                            G              ⁡                              (                s                )                                                    1              +                                                gD                  ⁡                                      (                    s                    )                                                  ⁢                                  G                  ⁡                                      (                    s                    )                                                                                =                                    ω              0              2                                                      s                2                            +                                                ω                  0                                ⁢                                                      1                    +                    gQ                                    Q                                ⁢                s                            +                              ω                0                2                                                                        (        2        )            
As shown in this equation, the Q-control reduces the Q value to Q/(1+gQ) to suppress possible resonance. For example, setting a gain ‘g’ at (2−1/Q) completely eliminates possible resonance.
An example in the case of a simple transfer function G(s) has been described. However, in the actual AFM, the scanner is a resonant system having plural resonant components connected in parallel. Accordingly, possible resonance cannot be easily suppressed as described above. For example, a transfer function for a resonant system having two parallel resonant components is expressed as follows.
                              G          ⁡                      (            s            )                          =                                                            A                1                            ⁢                              ω                1                2                                                                    s                2                            +                                                                    ω                    1                                                        Q                    1                                                  ⁢                s                            +                              ω                1                2                                              +                                                    A                2                            ⁢                              ω                2                2                                                                    s                2                            +                                                                    ω                    2                                                        Q                    2                                                  ⁢                s                            +                              ω                2                2                                                                        (        3        )            
In this equation, A1 and A2 denote the rates of magnitude of the respective components. Supposing that these components can be separately subjected to Q-control as shown in FIG. 2, the resonance of each component can be completely restrained (FIG. 2 shows a block diagram in which two resonant components can be individually subjected to Q-control). However, actual resonant systems have a single input and a single output. Consequently, it is impossible to perform individual Q-control. In other words, it is impossible to divide an input into two or to add outputs together as is the case with the configuration in FIG. 2.
Thus, actually, Q-control as shown in FIG. 3 must be performed. In FIG. 3, Q-control is performed on the sum of resonant components. Thus, the Q-control is incomplete as described in the following example.
FIG. 4 shows a transfer function of a resonant system having two resonant components (shown in the left side) and a transfer function obtained by performing Q-control using the configuration in FIG. 3 (shown in the right side). The upper side graph shows the relationship between angular frequency and gain. The lower side graph shows the relationship between angular frequency and phase. In this example, the original resonant system has resonant components, ω1=2π×100 kHz and ω2=2π×200 kHz (the left side in the FIG. 4).
As shown in FIG. 4, the Q-control has reduced the peak of the gain and thus resonances. However, the resonances have not been completely eliminated yet. Further, the valley of the phase has not been eliminated and remains as it is. With respect to an input signal having an almost central frequency between the two resonant frequencies, the phase is particularly delayed significantly.
The Q-control for the AFM is disclosed, for example, in Japanese Patent Laid-Open No. 2005-190228. The AFM in this document performs Q-control by detecting displacement of the scanner, and executing feedback processing on the basis of a detection signal (FIG. 17 of the document).
Japanese Patent Laid-Open No. 2005-190228 also proposes a Q-control technique using an equivalent circuit for the scanner (FIG. 19 of the document). The equivalent circuit has a transfer function equivalent to that of the scanner. An output from the equivalent circuit is processed as displacement of the scanner and Q-control is performed. A second-order low pass filter is illustrated as the equivalent circuit.
The conventional active damping technique has been explained above. As described in the above example, with the active damping such as the conventional active Q-control, it is not easy to sufficiently suppress vibrations of scanner of the AFM. For increasing the speed of the AFM, it is desirable to provide a more effective vibration reducing technique.
Further, the active damping is basically a technique for reducing the resonant peak. For increasing the speed of the AFM, if an available frequency band is increased or expanded by, for example, increasing a resonant point, such expanded band is more advantageous. However, such control has been generally impossible.
The background of the present invention has been described above taking the case of the scanner of the AFM. However, similar problems also occur with driving controlled objects other than the scanner of the AFM. For example, a vibration control technique is important for components other than the scanner of the AFM. Further, the vibration control technique is important for the SPMs other than the AFMs. Moreover, the similar requirement is seen in not only the SPMs but also various objects to be driven in a controlled manner.